Making a cylinder from a plane
You have several solutions, like the Spin tool or the Simple Deform modifier (with Bend option), or the Curve modifier, but I guess the Screw Modifier is the easiest way:


Create your profile shape, without any inner face. Keep in mind that the origin of the object will be the pivot of the rotation.
Assign your object a Screw modifier, choose the good axis, choose a 360° angle, and as many Steps as you want.
Keep a copy of your object before applying the modifier. Recalculate the Normals if necessary (ctrl N in Edit mode). You can also choose not to apply the Screw modifier, it will just make the edges sharpening a little bit longer at the end.
Assign your object a Subdivision Surface modifier. On the left panel (T) click on Tools > Shading > Smooth.
In Edit mode, add some edge loops to make your edges sharper (or, if you didn't apply the modifier, create some new vertices close to the existing ones: Select an edge, then create a vertice with ctrl R or W > Subdivide, then move the vertice along the edges with G G until it comes close to one of the existing vertices).